Electron. J. Differential Equations, Vol. 2020 (2020), No. 127, pp. 1-28.
Ingham type approach for uniform observability inequality of the semi-discrete
coupled wave equations
Dilberto da Silva Almeida Junior, Anderson de Jesus Araujo Ramos, Joao Carlos Pantoja Fortes, Mauro de Lima Santos
Abstract:
This article concerns an observability inequality for a system of coupled wave equations
for the continuous models as well as for the space semi-discrete finite difference
approximations. For finite difference and standard finite elements methods on uniform
numerical meshes it is known that a numerical pathology produces a blow-up of the constant
on the observability inequality as the mesh-size tends to zero.
We identify this numerical anomaly for coupled wave equations and we prove that there
exists a uniform observability inequality in a subspace of solutions generated by low
frequencies. We use the Ingham type approach for getting a uniform boundary observability.
Submitted November 14, 2019. Published December 22, 2020.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Coupled wave equations; positivity-preserving; semi-discretization;
Ingham's inequality.
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Dilberto da Silva Almeida Júnior
Ph D Program in Mathematics
Federal University of Pará
Augusto Corrêa Street, 01, 66075-110
Belém - Pará - Brazil
email: dilberto@ufpa.br, dilxingu@gmail.com
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Anderson de Jesus Araújo Ramos
Faculty of Sciences
Federal University of Pará
Raimundo Santana Street, s/n, 68721-000
Salinópolis - Pará - Brazil
email: ramos@ufpa.br
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João Carlos Pantoja Fortes
Ph D Program in Mathematics
Federal University of Pará
Augusto Corrêa Street, 01, 66075-110
Belém - Pará - Brazil
email: joaocarlos.fortes@yahoo.com.br
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Mauro de Lima Santos
Ph D Program in Mathematics
Federal University of Pará
Augusto Corr≖a Street, 01, 66075-110
Belém - Pará - Brazil
email: ls@ufpa.br
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